Let $\mathcal{H}$ be a hypergraph on a finite set V. A cover of $\mathcal{H}$ is a set of vertices that meets all edges of $\mathcal{H}$. If W is not a cover of $\mathcal{H}$, then W is said to be a noncover of $\mathcal{H}$. The noncover complex of $\mathcal{H}$ is the abstract simplicial complex whose faces are the noncovers of $\mathcal{H}$. In this paper, we study homological properties of noncover complexes of hypergraphs. In particular, we obtain an upper bound on their Leray numbers. The bound is in terms of hypergraph domination numbers. Also, our proof idea is applied to compute the homotopy type of the noncover complexes of certain uniform hypergraphs, called tight paths and tight cycles. This extends to hypergraphs known results on graphs.

让 $\mathcal{H}$是有限集V上的超图。一个盖的$\mathcal{H}$ 是一组顶点的集合，这些顶点与 $\mathcal{H}$。如果W不是$\mathcal{H}$，然后W¯¯被说成是一个noncover的$\mathcal{H}$。该noncover复杂的$\mathcal{H}$ 是抽象的单纯复形，其面是 $\mathcal{H}$。在本文中，我们研究了超图的非覆盖复合物的同源性。特别是，我们获得了其Leray数的上限。界线是根据超图控制数。同样，我们的证明思想被应用于计算某些统一超图的非覆盖复合物的同伦类型，称为紧密路径和紧密循环。这扩展到图上的超图已知结果。